A six-faced dice is loaded in such a way that an even number is three times as likely to occur as an odd number. (The dice is no longer `fair'.)
(a) If C is the event that an odd number occurs on a single toss of the die, find P(C).
(b) If E is the event that a number less than 4 occurs on a single toss of the die, find P(E).
(c) Let A be the event that an even number turns up on a single toss of the die and let B be the event that a number divisible by 3 occurs on a single toss of the die. Find P(A∪B), P(A∩B), P(A∪B') and P(A∩B'), where B' denotes the complement event of B.